OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 9 — Apr. 26, 2010
  • pp: 9266–9279

Light diffusion in a turbid cylinder. II. Layered case

André Liemert and Alwin Kienle  »View Author Affiliations


Optics Express, Vol. 18, Issue 9, pp. 9266-9279 (2010)
http://dx.doi.org/10.1364/OE.18.009266


View Full Text Article

Enhanced HTML    Acrobat PDF (915 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

This paper is the second of two dealing with light diffusion in a turbid cylinder. The diffusion equation was solved for an N-layered finite cylinder. Solutions are given in the steady-state, frequency, and time domains for a point beam incident at an arbitrary position of the first layer and for a circular flat beam incident at the middle of the cylinder top. For special cases the solutions were compared to other solutions of the diffusion equation showing excellent agreement. In addition, the derived solutions were validated by comparison with Monte Carlo simulations. In the time domain we also derived a fast solution (≈ 10ms) for the case of equal reduced scattering coefficients and refractive indices in all layers.

© 2010 Optical Society of America

OCIS Codes
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(170.5280) Medical optics and biotechnology : Photon migration

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: February 12, 2010
Revised Manuscript: April 7, 2010
Manuscript Accepted: April 14, 2010
Published: April 19, 2010

Virtual Issues
Vol. 5, Iss. 9 Virtual Journal for Biomedical Optics

Citation
André Liemert and Alwin Kienle, "Light diffusion in a turbid cylinder. II. Layered case," Opt. Express 18, 9266-9279 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-9-9266


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. A. Liemert and A. Kienle, “Light Diffusion in a N-layered Turbid Cylinder.I Homogeneous Case,” submitted.
  2. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic Press, New York, 1978).
  3. I. Dayan, S. Havlin, and G. H. Weiss, “Photon Migration in a Two-Layer Turbid Medium. A Diffusion Analysis,” J. Mod. Opt. 39, 1567–1582 (1992). [CrossRef]
  4. A. Kienle, M. S. Patterson, N. Dögnitz, R. Bays, G. Wagniàres, and H. van den Bergh, “Noninvasive Determination of the Optical Properties of Two-Layered Turbid Media,” Appl. Opt. 37, 779–791 (1998). [CrossRef]
  5. A. Kienle, T. Glanzmann, G. Wagnières, and H. van den Bergh, “Investigation of Two-Layered Turbid Media with Time-Resolved Reflectance,” Appl. Opt. 37, 6852–6862 (1998). [CrossRef]
  6. A. Kienle and T. Glanzmann, “In Vivo Determination of the Optical Properties of Muscle Using a Layered-Model,” Phys. Med. Biol. 44, 2689–2702 (1999). [CrossRef] [PubMed]
  7. J. M. Tualle, H. M. Nghiem, D. Ettori, R. Sablong, E. Tinet, and S. Avrillier, “Asymptotic Behavior and Inverse Problem in Layered Scattering Media,” J. Opt. Soc. Am. A 21, 24–34 (2004). [CrossRef]
  8. X. C. Wang and S. M. Wang, “Light Transport Modell in a N-Layered Mismatched Tissue,”Waves Rand. Compl. Media 16, 121–135 (2006). [CrossRef]
  9. A. Liemert and A. Kienle, “Light Diffusion in N-layered Turbid Media: Steady-State Domain,” J. Biomed. Opt.accepted. [PubMed]
  10. A. Liemert and A. Kienle, “Light Diffusion in N-layered Turbid Media: Frequency and Time Domains,” J. Biomed. Opt.accepted. [PubMed]
  11. G. Alexandrakis, T. J. Farrell, and M. S. Patterson, “Accuracy of the Diffusion Approximation in Determining the Optical Properties of a Two-Layer Turbid Medium,” Appl. Opt. 37, 7401–7409 (1998). [CrossRef]
  12. S-H. Tseng, C. Hayakawa, B. J. Tromberg, J. Spanier, and A. J. Durkin, “Quantitative Spectroscopy of Superficial Turbid Media,” Opt. Lett. 23, 3165–3167 (2005). [CrossRef]
  13. G. Alexandrakis, T. J. Farrell, and M. S. Patterson, “Monte Carlo Diffusion Hybrid Model for Photon Migration in a Two-Layer Turbid Medium in the Frequency Domain,” Appl. Opt. 39, 2235–2244 (2000). [CrossRef]
  14. M. Das, C. Xu, and Q. Zhu, “Analytical Solution for Light Propagation in a Two-Layer Tissue Structure with a Tilted Interface for Breast Imaging,” Appl. Opt. 45, 5027–5036 (2006). [CrossRef] [PubMed]
  15. A. H. Barnett, “A Fast Numerical Method for Time-Resolved Photon Diffusion in General Stratified Turbid Media,” J. Comp. Phys. 201, 771–797 (2004). [CrossRef]
  16. C. Donner and H. W. Jensen, “Rapid Simulations of Steady-State Spatially Resolved Reflectance and Transmittance Profiles of Multilayered Turbid Materials,” J. Opt. Soc. Am. A 23, 1382–1390 (2006). [CrossRef]
  17. F. Martelli, A. Sassaroli, S. Del Bianco, Y. Yamada Y, and G. Zaccanti, “Solution of the Time-Dependent Diffusion Equation for Layered Diffusive Media by the Eigenfunction Method,” Phys. Rev. E 67, 056623 (2003). [CrossRef]
  18. F. Martelli, A. Sassaroli, S. Del Bianco, and G. Zaccanti, “Solution of the Time-Dependent Diffusion Equation for a Three-Layer Medium: Application to Study Photon Migration through a Simplified Adult Head Model,” Phys. Med. Biol. 52, 2827–2843 (2007). [CrossRef] [PubMed]
  19. F. Martelli, S. Del Bianco, and G. Zaccanti, “Perturbation Model for Light Propagation through Diffusive Layered Media,” Phys. Med. Biol. 50, 2159–2166 (2005). [CrossRef] [PubMed]
  20. F. Martelli, S. Del Bianco, A. Ismaelli, and G. Zaccanti, Light Propagation through Biological Tissue and other Diffusive Media (SPIE Press, Bellingham, 2010).
  21. A. Kienle, “Light Diffusion Through a Turbid Parallelepiped,” J. Opt. Soc. Am. A 22, 1883–1888 (2005). [CrossRef]
  22. http://www.uni-ulm.de/ilm/index.php?id=10020200.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited